On Thursday, July 6, 2017 at 12:32:13 AM UTC-7, Bob Penoyer wrote:
I'm making a cabinet with shelves made of plywood. Some of the edges
of the shelves were burned while being cut on the table saw.

...I don't want to sand the edges of
the shelves since they're the correct dimension now. Will, say,
Titebond II hold the pieces together securely?

No. Sand the edges, to get the right surface for glue adhesion.
What causes 'burning' is a saw blade that's blunt or misaligned,
which rubs on the wood; this will collapse the wood fiber at the
cut, which impedes glue.

Coarse sandpaper, just enough to roughen the surface, is good for this.
I'd go for 80 grit and do it by hand.